1. Field of the Invention
The invention relates to a reflective grating for the optical diffraction of light rays and to methods for the manufacture of such a grating.
A grating is an optical surface with a periodic disturbance that disperses light by transmission or by reflection. The disturbance may be a slit (in the case of transmission), a line or a groove (in the case of reflection), or again it may be obtained by the printing of a sinusoidal fringe on a photographic plate (this is a sinusoidal grating).
If we consider a plane grating with grooves that are rectilinear parallel and equidistant along the width of the grating, by placing a pin-point source at the focal point of a collimator lens, the light is reflected in the regular direction of reflection (maxima value of central interference containing all the radiation from the source) and also in determined directions of maximum values of interference. The positions of the maximum interference depend on the wavelength.
This dispersive phenomenon is especially used in spectroscopy to obtain knowledge about the electronic structure of atoms and molecules on the basis of the optical spectral obtained: spectrographs, spectrometers and other instruments indeed use a monochromator with prism or grating associated with a receiver. The receiver may be a device for recording on a photographic plate (in the case of a spectrograph) or a photoelectrical detector, for example a photomultiplier (in the case of a spectrometer).
2. Description of the Prior Art
In recent applications, the monochromator has been used to study ultra-short optical pulses in the range of one picosecond. The object of these studies notably is to analyze the luminescence of semiconductor materials on the basis of the changes undergone in time by the spectrum at output of the monochromator.
For this purpose a laser 1 (FIG. 1) is used, producing ultra-short pulses in the range of one picosecond at a frequency of about 100 MHz, sent towards a semiconductor sample 2 for which it is sought to study the luminescence.
The incident light reaches the input collimator C1 of the monochromator 3 (vertical input slit, lens) and is then reflected and dispersed (mirrors M1, M4, M3, grating R) to give the output spectrum at the output collimator C2 (horizontal output slit, lens).
At output of the monochromator a streak camera is placed. The high temporal resolution of this streak camera enables analysis of the phenomena in the one-picosecond range. To put it in a simplified way, the camera (not shown) has a scanning tube with a photocathode and a grid electrode between which there prevails an intense electrical field. The camera also has a deflection circuit, a photomultiplier and a phosphorescent screen.
The general principle of the functioning of the camera is as follows: an input slit and a lens focus the incident light on the photocathode of the tube. The photons converted into electrons are accelerated and led towards the deflection field where they are scanned at high speed in the direction perpendicular to the input slit (the vertical direction in this example since the input slit is horizontal). They then go into the photomultiplier and form the optical image by bombarding the phosphorescent screen.
The time at which the electrons are liberated from the photocathode may be determined by their angle of deflection given, in the example, by their vertical position on the phosphorescent screen. Thus, the temporal axis corresponds to the axis perpendicular to the input slit on the phosphorescent screen of the camera.
By using, as incident light, the output spectrum of the monochromator on the vertical output slit of this monochromator, the axis of wavelengths is obtained, constituting a second dimension on the phosphorescent screen along the axis perpendicular to the temporal axis.
Thus, in the example, there is the temporal axis, which is the horizontal axis on the phosphorescent screen, and the axis of wavelengths, which is the vertical axis on the phosphorescent screen.
In order that the device may work, it is again necessary to synchronize the scanning (or deflection) voltage of the streak camera with the arrival of the electronics in the deflection field. For example, a photodiode-based detector 5 is used. A part of the incident light (plate 6) is deflected towards this detector which gives the camera 4 an activation signal (7) to synchronize the scanning voltage of the deflection circuit of the camera.
Streaks can then be observed on the output screen of the streak camera 4. These streaks show the changes undergone by the luminescence emitted by the sample excited by the laser 1, as a function of the wavelength (horizontal axis) and of time (vertical axis). The luminescence may thus be analyzed by an output read circuit comprising, for example, a vidicon camera 8 placed at output of the streak camera 4 that delivers a video signal to peripheral circuits such as a video monitor 9, a temporal analyzer 10, etc.
The device described enables the carrying out of time-resolved spectroscopy.
One problem encountered in the analysis of the image obtained is related to the grating of the monochromator 3.
Indeed, the grating which spectrally disperses a light pulse also temporally widens the pulse because of the difference in optical path. The phenomenon is shown in FIG. 2 for two rays each arriving at one of the two ends of the grating.
In the example, the grating is one with grooves spaced out at a pitch d. It has a width D on which there are made grooves that are parallel and equidistant (with the pitch d). The density of grooves per millimeter is referenced N=1/d.
The groove could be a simple etched line. In the example, it has a triangular cross-section. The rays reach the surface, for example AB, inclined by an angle i with reference to the plane P of the grating.
The profile of the groove affects the distribution of the light energy in the different orders of interference. The triangular cross-sectioned profile is particularly used in monochromators for its ability to concentrate the light energy in a single order of interferences.
Let us now take two light rays L1 and L2 with a wavelength .lambda. reaching the grating at one and the same incidence .alpha. with respect to the normal to the plane P of the grating. The ray L1 reaches the end A, the ray L2 reaches the other end B. They are diffracted at the angle of diffraction .beta. (with respect to the normal to the plane P of the grating).
The equation of the gratings can then be written as follows: EQU m.lambda.=d(sin .alpha.+sin .beta.)=1/N(sin .alpha.+sin .beta.)(1)
where m is the order of interferences considered (with m as a positive or negative integer).
The optical path travelled by L1 will be longer in the example than that travelled by L2. The difference .DELTA..gamma. is written in the case of FIG. 2 as follows: EQU .DELTA..gamma.=.gamma.2+.gamma.1=D(sin .alpha.+sin .beta.) (2)
namely, in using the equation (1): EQU .DELTA..gamma.=DmN.lambda.
The time difference for the first order of interference (m=1) is then written as follows: EQU .DELTA.t=.DELTA..gamma./C=DN.lambda./C (3)
The temporal dispersion .DELTA.t for a given wavelength .lambda. and a determined order of interference m depends only on the width D and on the density N of lines (grooves) of the grating. In one digital example related to the study of ultra-short pulses (picoseconds), we have:
D=60 mm (millimeters) PA1 N=1200 lines/mm PA1 d=1/N=0.83 .mu.m (micrometers). PA1 .lambda.=0.76 .mu.m, we then have for m=1: PA1 .DELTA.t=DN.lambda./C=60.1200.0,76.10.sup.-6 /3.10.sup.8 PA1 .DELTA.t=182 picoseconds. PA1 the preparation of k identical rectangular triangle shims made of glass or silica; PA1 the assembling of k shims on a glass or silica plate so that the hypotenuses of said shims form k juxtaposed planes having the same inclination i with respect to the plane of the plate; PA1 a sub-grating being placed on the hypotenuse of each of the shims.
giving
For a monochromatic source with a wavelength
Given the order of magnitude of the phenomena to be observed (pulses of the order of one picosecond), this temporal dispersion is highly inconvenient.
We might then be tempted to reduce the characteristic magnitudes N and D of the grating.
For example, by reducing the width D of the grating to 4 millimeters, a temporal dispersion .DELTA.t of 12 picoseconds is obtained.
If the density of lines is reduced by half (N=600 lines/mm), we obtain .DELTA.t=6 picoseconds.
It is however necessary to obtain the greatest possible luminosity in the output image. This is already what has led to prefer a particular profile for the grooves of the grating (the triangular cross-section) as explained here above.
Now, reducing the width of the grating means also reduces the output luminosity. This is unacceptable.
It is also necessary to obtain the greatest spectral resolution. The spectral resolution R of a grating gives a numerical value of its ability to enable a distinction to be made between two wavelengths that are very close to each other with a difference between them of .DELTA..lambda.: EQU R=.lambda./.DELTA..lambda.=m.D.N (4)
For the first order of interference (m=1), we therefore have: EQU R=.lambda./.DELTA..lambda.=D.N (5)
Furthermore, the following relationship: EQU .DELTA.t..DELTA..lambda.=.lambda..sup.2 /C (6)
limits the spectral resolution for a given temporal dispersion .DELTA.t.
Thus, therefore, if N and L are chosen so as to obtain a minimum temporal dispersion, the spectral resolution of the grating is then reduced.
In the digital example given here above, for .lambda.=0.76 .mu.m, with N=1200 lines/mm and D=60 mm, it has been seen that we then have .lambda.t=182 picoseconds. We then have .DELTA..lambda.=.lambda..sup.2/ .DELTA.t.c=0.01 nanometers.
However, if N=600 lines/mm and D=4 mm, it has been seen that we then have .DELTA.t=6 picoseconds but then .DELTA..sup.2 /.DELTA.t.C=0,32 nanometers: the spectral resolution R=.DELTA..lambda./.lambda. is then considerably reduced. There is therefore always an inevitable compromise between the spectral resolution and the temporal dispersion. However, the monochromator itself limits the spectral resolution because of the width of the input slit and the spectral resolution of the detection system formed by the streak camera 4 and the vidicon tube 8 (FIG. 1). It is therefore necessary to reduce the spectral resolution of the grating so as to adapt it to the spectral resolution of the monochromator or more generally to the desired spectral resolution. The temporal dispersion is thus diminished at the same time.